Nelson Martins-Ferreira ; Andrea Montoli ; Manuela Sobral - On some categorical-algebraic conditions in S-protomodular categories

lmcs:2552 - Logical Methods in Computer Science, September 1, 2017, Volume 13, Issue 3 - https://doi.org/10.23638/LMCS-13(3:18)2017
On some categorical-algebraic conditions in S-protomodular categoriesArticle

Authors: Nelson Martins-Ferreira ORCID; Andrea Montoli ; Manuela Sobral

    In the context of protomodular categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cartesian closedness and algebraic coherence. The recent notion of S-protomodular category, whose main examples are the category of monoids and, more generally, categories of monoids with operations and Joónsson-Tarski varieties, raises a similar question: how to get a description of S-protomodular categories with a strong monoid-like behavior. In this paper we consider relative versions of the conditions mentioned above, in order to exhibit the parallelism with the "absolute" protomodular context and to obtain a hierarchy among S-protomodular categories.


    Volume: Volume 13, Issue 3
    Published on: September 1, 2017
    Accepted on: May 19, 2017
    Submitted on: September 1, 2017
    Keywords: Mathematics - Category Theory,18G50, 02C05, 08C05, 18D35
    Funding:
      Source : OpenAIRE Graph
    • Center for Mathematics, University of Coimbra; Funder: Fundação para a Ciência e a Tecnologia, I.P.; Code: UID/MAT/00324/2013
    • Centre for Rapid and Sustainable Product Development; Funder: Fundação para a Ciência e a Tecnologia, I.P.; Code: UID/Multi/04044/2013

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